If you use pkexec lightdm-settings it will create this file, though there might be more in it (depends on what you change).
/etc/lightdm/slick-greeter.conf
[Greeter]
background=/usr/share/backgrounds/mushroom-moon.jpg
This will change the background for the login screen. If you want to change the background for the lock screen, you can do it through the screensaver.
Classic and Compact menus:
System → Preferences → Look and Feel → Screensaver → Background picture for the lock screen (at the bottom of the window)
Brisk menu:
Preferences → Screensaver → Background picture for the lock screen